Answer:
Step-by-step explanation:
Definition of Square: a parallelogram whose area is equal to the product of its sides. The circle is a plane figure whose area is calculated by the formula r².
The length of the side of the square is .
Given:
The radius of the circle is = r cm.
Length of the side of square = a cm
Now,
Area of Square is = a²
Area of Circle = r²
Since, given that radius of a circle is equivalent to the length of the square, such that:
a² = r²
a² = r²
a =
a =
Thus, the value of the length of the square is r√π.
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Which table represents a quadratic relationship?
A .x -2 -1 0 1 2 3
f(x) 4 2 1 0.5 0.25 0.125
B. x -7 -6 -5 -4 -3 -2
f(x) 135 128 105 72 35 0
C. x -2 -1 0 1 2 3
f(x) -23.4 -23.2 -23 -22.8 -22.6 -22.4
D. x -1 0 1 2 3 4
f(x) 90 56 26 0 -22 -40
In each case, the x-values are equally-spaced. Thus looking at second differences will tell you if the relation is quadratic. If the second differences are non-zero and constant, then the values have a quadratic relationship.
A. First differences are 2-4 = -2, 1-2 = -1, 0.5-1 = -0.5. Second differences are -1-(-2) = 1, -0.5-(-1) = 0.5. Since 1 ≠ 0.5, this relation is not quadratic. (It is exponential with a base of 1/2.)
B. First differences are 128-135 = -7, 105-128 = -23, 72-105 = -33. Second differences are -23-(-7) = -16, -33-(-23)=-10. Since -16 ≠ -10, this relation is not quadratic. (It is cubic, since 3rd differences are constant at +4.)
C. First differences are -23.2-(-23.4) = 0.2, -23.0-(-23.2) = 0.2, -22.8-(-23.0) = 0.2. Second differences are zero, so this is not a quadratic relation. (It is linear, with a slope of 0.2.)
D. First differences are 56-90 = -34, 26-56 = -30, 0-26 = -26. Second differences are -30-(-34) = 4, -26-(-30) = 4. These are constant (=4), so the relation is quadratic.
The appropriate choice is ...
... D. x -1 0 1 2 3 4
... f(x) 90 56 26 0 -22 -40
Answer: D. x -1 0 1 2 3 4
f(x) 90 56 26 0 -22 -40
Step-by-step explanation:
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Which is the formula for the volume of a sphere with diameter d?
A. S= 4πd²
B. S= πd²
C. S= [tex] \frac{4}{3} [/tex]πd³
D. S= [tex] \frac{1}{6} [/tex]πd³
Explain why 0.04 divided by 3.6 has the same answer as 4 divided by 360
what is the product? 4k+2/k^2-4*k-2/2k+1
Find the area of A cylinder has a volume of 175 cubic units and a height of 7 units. The diameter of the cylinder is
The function f(x)= 2 x 5^x can be used to represent the curve through the points (1, 10), (2, 50), and (3, 250). What is the multiplicative rate of change of the function ?
Which of the following would be a factor of the equation above.
An angle measures 4.3 radians To the nearest degree, what is the measure of the angle? degrees
The measure of the given angle in degrees is:
246 degrees
Step-by-step explanation:We are given a angle measure in radians.
We have to convert the given angle measure to degrees.
We know the conversion that:
π radians= 180°
⇒ 1 radians= 180°/π
Hence, the value of 4.3 radians will be, we multiply both side of the equation by 4.3 :
4.3 radians=246.372°
Hence, to the nearest degree i.e. to the whole number of a degree we get the value of:
4.3 radians= 246°
Rosalie wants to get the entire outside of a cabinet laminated. The cabinet is 3 feet long, 2 feet wide and 5 feet high. The cost of lamination is $2 per square foot. How much will it cost Rosalie to get the cabinet laminated?
To laminate the cabinet, the total surface area is calculated and multiplied by the cost per square foot. The cabinet has a surface area of 62 square feet, and with a lamination cost of $2 per square foot, it will cost Rosalie $124.
To calculate the cost for laminating the outside of a cabinet, we first need to find the total surface area to be laminated. Since the cabinet is a rectangular prism, we can use the surface area formula for a rectangular prism: Surface Area = 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height. In this case, l = 3 ft, w = 2 ft, and h = 5 ft.
Surface Area = 2(3 ft)(2 ft) + 2(3 ft)(5 ft) + 2(2 ft)(5 ft)
Surface Area = 2(6) + 2(15) + 2(10)
Surface Area = 12 + 30 + 20
Surface Area = 62 square feet
Now to find the total cost, we multiply the surface area by the cost per square foot: Total cost = Surface Area times Cost per square foot.
Total cost = 62 sq ft times $2/sq ft
Total cost = $124
Therefore, it will cost Rosalie $124 to get the cabinet laminated.
The pair of points is on the graph of an inverse variation. Find the missing value. (1.6, 6) and (8, y) 0.03 30 1.2 0.83
Answer: 1.2
Step-by-step explanation:
The formula for inverse variation is given by :-
[tex]x_1y_1=x_2y_2[/tex]
The given points : (1.6, 6) and (8, y)
It means at x = 1.6 , y=6 .
To find the value of y at x=8 , we substitute [tex]x_1=1.6,\ y_1=6\, \text{ and}\ x_2=8,\ y_2=y[/tex] in the above formula , we get
[tex]1.6\times6=8y\\\\\Rightarrow\ y=\dfrac{1.6\times6}{8}\\\\\Rightarrow\ y=1.2[/tex]
Thus, the missing value = 1.2
Find the value of x.
Write a complete sentence that states the type of transformation that was performed and explains the transformation in detail. Quadrilateral EFGH is the image.
ABCD A(-4,-1)B(-1,-4)C(-2,-8)D(-5,-4)
EFGH
E(0,-6)F(3,-9)G(2,-13)H(-1,-9)
Answer for number 5?
Prism A is similar to Prism B. The volume of Prism A is 2080 cm³.
What is the volume of Prism B?
A.260 cm³
B.520 cm³
C.1040 cm³
D.16,640 cm³
Will give brainliest answer!
Final answer:
Prism B's volume is 8 times larger than Prism A's volume due to the dimensions being twice as large. Given the volume of Prism A as 2080 cm³, the volume of Prism B is 16640 cm³.
Explanation:
The student is asking about the volume of similar prisms. When two prisms are similar, their volumes are proportional to the cube of the ratio of their corresponding linear dimensions. In this case, Prism B is similar to Prism A, and the ratio of the volumes is given in the problem. Specifically, the volume of Prism B is 4 times the volume of Prism A because the dimensions of Prism B are twice that of Prism A, making the volume 23 or 8 times greater. However, you've also provided that the volume of Prism B is 4 times that of Prism A, this seems to be a conflict in the information, and there's an issue with typos in the provided content which makes it inconsistent (2L3 versus 213, 213). Based on the correct proportion which should be 8 times, if the volume of Prism A is 2080 cm3, then the volume of Prism B would be 2080 cm3 multiplied by 8 (8L3/L3), yielding 16640 cm3.
Is the square root of eight a rational or irrational number
ASAP PLEASE:
Segment RS is congruent to segment DF. Which congruence statement is true?
- RS ≅ DF
- RS ≅ SFD
- RS ≅ SF
- RS ≅ RD
Answer:
A. [tex]\text{ Arc RS}\cong \text{Arc DF}[/tex]
Step-by-step explanation:
We have been given a circle and we are told that segment RS is congruent to segment DF.
We can see that segment RS corresponds to arc RS and segment DF corresponds to arc DF.
As both segments are congruent, therefore, both arcs will be congruent as well.
We can represent this information as:
[tex]\text{ Arc RS}\cong \text{Arc DF}[/tex]
Therefore, option A is the correct choice.
Boyles law involves the pressure and volume of gas in a container. It can be repersented by the formula p sub 1 v sub 1= p sub 2 v sub 2. When the formula is solved for p sub 2, the results is
Boyle's Law can be rearranged to solve for p sub 2 (final pressure) using the formula p sub 2 = p sub 1 v sub 1 / v sub 2. This shows the inverse relationship between pressure and volume of gas at a constant temperature.
Explanation:The question is asking to solve the formula representing Boyle's Law (p sub 1 v sub 1 = p sub 2 v sub 2) for p sub 2. Boyle's Law states that the pressure and volume of a gas have an inverse relationship when temperature is held constant. To solve for p sub 2, you rearrange the formula to be p sub 2 = p sub 1 v sub 1 / v sub 2. This formula means that the final pressure (p sub 2) equals the initial pressure (p sub 1) times the initial volume (v sub 1), all divided by the final volume (v sub 2). Therefore, if the volume increases, the pressure decreases, and if the volume decreases, the pressure increases, keeping the gas's temperature constant.
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If the polygon shown below is a regular nonagon what is the value of x?
The measure of angle x is 40 degrees and this can be determined by using the formula of the sum of interior angles of a polygon.
Given :
A regular nonagon.
The sum of interior angles of a polygon is given by the equation:
= (n - 2)180 --- (1)
where 'n' is the total number of sides of the polygon.
Given that the polygon is the regular nonagon that means the total number of sides is 9.
Now, substitute the value of 'n' in the equation (1).
= (9 - 2)180
= [tex]1260^\circ[/tex]
Now, divide the above expression by 9 in order to get the value of one interior angle.
[tex]= \dfrac{1260}{9}[/tex]
= [tex]140^\circ[/tex]
Now, the sum of one interior angle and the angle x is equal to 180 degrees that means:
140 + x = 180
x = [tex]40^\circ[/tex]
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which rule describes the translation PQR --> P'Q'R'?
Use the rules of significant figures to answer the following question:
67.31 - 8.6 + 212.198
A. 270.9
B. 271
C. 270.908
D. 270
Answer:
A. 270.9
Step-by-step explanation:
We know that the rule of significant figures for addition and subtraction states that 'the number of places after the decimal point in the result is equal to the least number of decimal places in each term.'
So, 67.31 - 8.6 + 212.198 = 67.31 + 212.198 - 8.6 = 279.508 - 8.6 = 270.908
Now, the resultant number is 270.908
Using the rule of significant figures, we get that, the number of places after the decimal point in 270.908 will be equal to the least number of decimal places i.e. 1 ( in 8.6 )
Hence, 67.31 - 8.6 + 212.198 = 270.9
Orlando bought a new couch for 2,736 , using the furniture store's finance plan. He will pay $114 a month for 24 months. Which equation can Orlando use to find out how much money he still owes after each month of the plan?
A sandwich shop uses the box size shown to pack boxed lunches. They have determined that they need to use bigger boxes. If the side lengths of the square faces are changed to 7 inches, by how much will this increase the volume of the box?
Answer:
240 cubic cm
Step-by-step explanation:
Volume of the box before increament in sides = length*width*height
Length= 5 in.
Width=5 in.
Height = 10 in.
Putting these vales in formula
Volume of box = 5*5*10
=[tex]250cm^{3}[/tex]
Now If the side lengths of the square faces are changed to 7 inches,
So, Length will be 7 in.
Width will be 7 in.
So, new volume = 7*7*10
=[tex]490cm^{3}[/tex]
Thus increase in volume = 490-250 =240
Hence by 240 cubic cm will this increase the volume of the box
Could use some help!
An architect created plans for a house using a scale factor of 1:16 . In the plans, the floor of the house has an area of 7 square feet. What is area of the floor in the actual house? Enter your answer in the box.
A rectangle has a length of 6 inches and a width of 3 inches.
What is the effect on the perimeter when the dimensions are multiplied by 8?
The perimeter is increased by a factor of 8.
The perimeter is increased by a factor of 24.
The perimeter is increased by a factor of 64.
The perimeter is increased by a factor of 256.
This figure is made up of a triangle and a semicircle.
What is the area of this figure?
Use 3.14 for pi. Round only your final answer to the nearest tenth.
Enter your answer, as a decimal, in the box.
$7.80/hour = ____ cents/minute?
If g(x) is the inverse of f(x) and f(x) = 4x+12 what is g(x)?
Answer:
Inverse function: A function g is the inverse of a function f if whenever y=f(x) then x=g(y).
In other words, we can write this in terms of the composition of f and g as g(f(x))=x.
For any input x, the function corresponding to f spits out the value y=f(x)=4x+12.
Now, we want to find the inverse function g(x)=[tex]f^{-1}[/tex] that takes the value y as an input and spits out x as the output.
In other words, y=f(x) gives y as a function of x and we want to find [tex]x=f^{-1}(y)[/tex] that will give us x as a function of y.
Given,the expression y=4x+12 for y as a function of x and solve for x.
Subtract 12 from both sides we get;
y-12 = 4x+12-12
Simplify:
y-12 = 4x
Divide by 4 to both sides we get;
[tex]\frac{y-12}{4} =\frac{4x}{4}[/tex]
Simplify:
[tex]x=\frac{1}{4}y - 3[/tex]
therefore, [tex]x = f^{-1}(y) = \frac{1}{4}y-3[/tex]
since, g(x) is the inverse of f(x)
⇒[tex] g(x)=\frac{1}{4}x-3[/tex]
Now, verify that g(x) is really the inverse of f(x), we should show that the composition of f and g doesn't do anything to the input.
[tex](g o f)(x) = g(f(x)) = g(4x+12) = \frac{1}{4}(4x+12) -3 = x+3 -3[/tex]
Simplify:
g(f(x)) = x for all x
⇒ g(x) is the inverse of f(x)
Therefore, [tex] g(x)=\frac{1}{4}x-3[/tex]
Using inverse functions, it is found that that:
[tex]g(x) = \frac{x - 12}{4}[/tex]
To find the inverse function, we exchange x and y in the original function, then isolate f.
The function f(x) is given by:
[tex]f(x) = 4x + 12[/tex]
Function g(x) is the inverse of f(x), then:
[tex]y = 4x + 12[/tex]
[tex]x = 4y + 12[/tex]
[tex]4y = x - 12[/tex]
[tex]y = \frac{x - 12}{4}[/tex]
[tex]g(x) = \frac{x - 12}{4}[/tex]
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What form of a quadratic function would be graphed having the vertex at the same point as the y-intercept?
find p(-3) and p(5) for the function p(x)=4x^4+8x^3-2x^2+13x+10